The literature cited by Unger is uniformly confused. I can’t speak for the German scholarship, however.
The question of the Axial Age can’t be solved by standard science/social science/and/or religious interpretations.
Here are a few things needed to make sense of the phenomenon: its data shows synchronous emergence in five Eurasian zones, meaning no one zone can influence the others by diffusion. That’s a heart attack for the sociology of religion.
The data is not about religion! It is about ‘cultural evolution’ in a differential time-slice, so to speak. The Axial era of archaic Greece is actually the key to the whole game.
the interval given by Jaspers is too long, leading to the inclusion of data that is not like that of the core Axial Age…The better interval would be 900 to 600 to 400. What does this mean? There is a generating interval three centuries in length, roughly, and then possibly a take-off phase in its wake. But in general the case of archaic ‘Israel/Judah’ shows the clearest case: there is a clear interval of roughly three centuries, longer or shorter by not much, from 900BCE to 600BCE. The evidence here is remarkable to say the least. Before the Exile we see the remnant Judah(‘Israel’) with its prophetic tradition an a ‘not yet final’ draft of the Old Testament. Then, in absolute extraordinary precision, the bad guys swoop down once again on the Israelites, taken into Exile right at the rough endpoint of the three century interval, where they blend their monotheism of semitic origin with another monotheism of Aryan origin, and then the Israelites return to their homeland with the about to be completed Old Testament now with added materials, including the Zoroastrian apocalyptic thematic to become notorious in the revolutionary strategy of Israel versus Rome. (note how the interval from 600 to 400 fits here: the period down to 400 shows the ‘age of revelation’ (not my term) to be weakening as the final text of the Old Testament is collated. This mutual blending is the absolute tour de force of world history. This is the exception that proves the rule of no diffusion of parallel zones.
You have to toss linear sociology of religion out of the window here. Some higher design element is at work.
More generally, however the Axial Age is not about religion. The case of Axial Age Greece is so striking as to be almost beyond amazement.
There is a lot more here, but we can see that the usual analysis won’t work.
This situation shows how what we call modernity is of a piece with the overall dynamic. But the situation is different and implicates modern political revolution more than religion/reformation.